Geometric+Sequences+2C-1

__Geometric Sequences__
A geometric sequence is a specific pattern in which you multiply or divide by the same number every time in order to get the next term in the sequence. toc Example 1 Here is an example of a Geometric Sequence. {2, 4, 8, 16 , 32,.....}

__General Formula__
The general formula for geometric sequence is the following: math f(x)= k*m^x math

where, f(x), is the value of the xth term of the sequence. k, is the initial value or 0th term. m, is the Common Ratio or Multiplier x, is the term of the sequence that you are trying to find.

Find the 6th term of this geometric sequence. {2, 4, 8, 16 , 32,.....} ||= ** Explanation ** || math f(x)= 2*2^{(x)} math || k is the initial value which is 2. m is the Common Ratio or Multiplier which is also 2. x is the term of the sequence that you are trying to find which is 6. || math f(6)= 2*2^6 math
 * = ** Example 2 **
 * The formula for this sequence is:
 * The 6th term in this sequence is:

math f(6)= 2 * 64 math

math f(6) = 128 math || x is the term of the sequence that you are trying to find which is 6. ||

__Graphing a Geometric Sequence__
All geometric sequences have the same shape when graphed. The graph of a geometric sequence is a curve.

Example 3 f(x)=2*2^x math ||= 2 ||= 4 (2x2) ||= 8 (4x2) ||= 16 (8x2) ||= 32 (16x2) ||= 64 (32x2) ||= **128** (64x2) ||
 * = x ||= 0th term ||= 1st term ||= 2nd term ||= 3rd term ||= 4th term ||= 5th term ||= 6th term ||
 * = math

__Further Discussion__

 * What's the advantage of having a formula?
 * What does the graph of a geometric sequence tell us?